In this study, novel materials have been obtained via a dual covalent and ionic crosslinking strategies, leading to the formation of a fully interpenetrated polymeric network with remarkable mechanical performances as drug delivery platforms for dermal patches. The polymeric network was obtained by the free-radical photopolymerization of N-vinylpyrrolidone using tri(ethylene glycol) divinyl ether as crosslinker in the presence of sodium alginate (1%, weight%). The ionic crosslinking was achieved by the addition of Zn2+, ions which were coordinated by the alginate chains. Bentonite nanoclay was incorporated in hydrogel formulations to capitalize on its mechanical reinforcement and adsorptive capacity. TiO2 and ZnO nanoparticles were also included in two of the samples to evaluate their influence on the morphology, mechanical properties and/or the antimicrobial activity of the hydrogels. The double-crosslinked nanocomposite hydrogels presented a good tensile resistance (1.5 MPa at 70% strain) and compression resistance (12.5 MPa at a strain of 70%). Nafcillin was loaded into nanocomposite hydrogel films with a loading efficiency of up to 30%. The drug release characteristics were evaluated, and the profile was fitted by mathematical models that describe the physical processes taking place during the drug transfer from the polymer to a PBS (phosphate-buffered saline) solution. Depending on the design of the polymeric network and the nanofillers included, it was demonstrated that the nafcillin loaded into the nanocomposite hydrogel films ensured a high to moderate activity against S. aureus and S. pyogenes and no activity against E. coli. Furthermore, it was demonstrated that the presence of zinc ions in these polymeric matrices can be correlated with the inactivation of E. coli.